CN1549069A - Statistical tolerancing - Google Patents

Abstract

A process of establishing valid statistical dimensional tolerance limits for designs of detail parts that will enable accurate prediction of an economically acceptable degree of non-conformance of a large flexible end item assembly, having a set of predetermined dimensional tolerances, made from the detail parts, wherein the detail part tolerances are enlarged substantially compared to tolerances that would be necessary using an arithmetic 'worst case' approach to remain within the end assembly tolerances while remaining within preestablished stress limits of the parts. A preferred assembly sequence for assembling the parts into the assembly is selected and validated. Locations, numbers and size of coordination features to be machined in said detail parts are selected, by which the parts are located relative to each other and fastened together to form the assembly. Individual part statistical dimensional tolerances are established as a fabrication requirement for the parts that enable the parts to be economically produced and assembled into assemblies that meet the predetermined assembly dimensional tolerances.

Description

Statistical tolerance is determined method

The application is to be that June 21, application number in 1996 are 96196485.5, are entitled as the dividing an application of patented claim of " statistical tolerance is determined method " applying date.

The present invention relates to make the large scale compliant member to satisfy the method for final assembly parts tolerance, determine to go through the method for the tolerance route of all approach parts from final assembly parts characteristic portion, and the method for in the tolerance route, selecting the tolerance of position components feature.The present invention has also considered the relation of component tolerances and instrument tolerance and the application of correction factor, and this correction factor influences parts operation mean shift.

Determine in the method in traditional arithmetic tolerance, just the limit deviation of all tolerances in the tolerance group by the drawing tolerance added up, thereby the assembling deviation during to " the worst incident " is made a prediction.It is pointed out that if the parts of making drop in the margin tolerance, and be correct, utilize " the worst incident " method can guarantee that the qualification rate of assembly parts is 100% the analysis of assembling.

Statistical tolerance determines that method utilized assembly parts hardly or not with comprehensive this fact of " the worst incident " mode, and accepts a spot of assembly parts and may not satisfy tolerance.According to this method, component tolerances can be amplified, because can prove that tolerance is very little with the comprehensive statistical probability of " the worst incident " mode.The analysis showed that, utilize statistical tolerance to determine method, adopt its bigger component tolerances that can allow, the only a few assembly parts that tolerance is not satisfied in the economic benefit that is obtained comparison carry out secondary processing even eliminate the cost of being paid and want high.When utilizing statistical tolerance to determine the requirement of method design drawing, relate to design proposal more and calculate and the parts verification scheme, so only some critical sizes are just determined with statistical method usually.

At production large scale compliant member and assembly parts, during such as aircraft, adopt the assembly method of a kind of being called " determinacy assembling ", it has avoided using traditional " rigidity frock ".The U.S. Patent application No.07/964 that is entitled as " wallboard and body assembling (Panel and FuselageAssembly) " that Micale and Strand submitted on October 13rd, 1992,533 disclose a kind of example that is used to make " the determinacy assembling " of airframe wallboard and body.Munk and Strand on March 22nd, 1996 submit to be entitled as another example that " determinacy wing assembling (Determinant Wing Assembly) " U.S. Provisional Patent Application 60/013986 discloses " the determinacy assembling " that be used for making wing in the aircraft industry.For guaranteeing that the assembling with the assembly parts of determinacy assembly method design is qualified, cope with tolerances is analyzed, and can realize to guarantee the tolerance that is marked on the drawing, and preferred fabrication scheme/assembly process is supported.For the acceptance probability of being made of assembly parts the attainable parts of its tolerance is estimated, must carry out TOLERANCE ANALYSIS with statistical method to the typical tolerances combination of aircraft assembly parts.

" totally " speech of the parts of making is used for describing the set of numeral or numerical value here, and " totally " measured value or observed reading by parts constituted.Herein, the overall and measured value of parts is described by the distribution of these numerical value.This distribution is provided by frequency distribution, probability distribution or density function f (x) usually.Describing two overall parameters is average μ and standard deviation, σ ²Then be called population variance.These two parametric representations overall center and pericentral bias property.More particularly, represent that with f (x) these two parameters are exactly:

For the discrete magnitude situation, totally constitute, and to the continuous quantity situation, population size is very big by many limited numerical value, to represent conveniently with serial number, the distribution of numerical value is described with density function f (x).If totally by normal distribution, then the measured value of parts will be by distribution shown in Figure 1 and proportional cutting apart substantially.

When population size was very big, it is all observed usually was unpractical, or uneconomic.On the contrary, people extract random sample, infer the interested feature that about overall on the basis that sampling is tested.The purpose that great majority are added up sampling observation is to utilize from the overall middle information summary that random sample comprised that extracts to go out overall feature.For example, according to sample X ₁..., X _nInfer population parameter μ and σ ²The time, calculate the respective sample estimator, i.e. sample average:

$\stackrel{\&OverBar;}{X}=\frac{{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">X</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">X</figure-callout>}}_2+...+X_n}{n}=\frac{1}{n}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{X}_j$

And sample variance

${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">S</figure-callout>}}^2=\frac{{(X_1-\stackrel{\&OverBar;}{X})}^2+{(X_2-\stackrel{\&OverBar;}{X})}^2+...+{(X_n-\stackrel{\&OverBar;}{X})}^2}{n-1}=\frac{1}{n-1}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{(X_1-\stackrel{\&OverBar;}{X})}^2$

Herein, at S ²Definition in, consider estimator S ²Unbiasedness, divisor adopts n-1.For large sample, divisor is that n or n-1 are unimportant.

A basic assumption of the statistical tolerance analytical approach of being inquired into here is that the characteristic dimension of the parts of manufacturing can be described with normal distribution.The probability density function of normal distribution is:

$f\left(x\right)=f_{\mathrm{\&mu;},\mathrm{\&sigma;}}\left(x\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">e</figure-callout>}}^{\frac{1}{2}[(x-\mathrm{\&mu;})/\mathrm{\&sigma;}{]}^2}$

X equals 1 from-∞ to+normal curve was covered down when ∞ changed whole area.(area that f (x) covers down between a≤b) equals the ratio of the parts characteristic dimension between a and b at any 2 a and b.

Because normal probability density function is non-integrable in by the closed interval that limit value is defined, fall into the probability of the parts characteristic dimension between the limit value or ratio usually by looking into μ=0, the standardized normal distribution table of σ=1 draws, and this is to be undertaken by following standardization.

Average is μ; Standard deviation is that the overall random element of the normal distribution of σ is represented with X, and the population proportion that then falls into these elements of [a, b] is:

$P(a\&le;X\&le;b)=P(\frac{a-\mathrm{\&mu;}}{\mathrm{\&sigma;}}\&le;\frac{X-\mathrm{\&mu;}}{\mathrm{\&sigma;}}\&le;\frac{b-\mathrm{\&mu;}}{\mathrm{\&sigma;}})$

$=P(\frac{a-\mathrm{\&mu;}}{\mathrm{\&sigma;}}\&le;Z\&le;\frac{b-\mathrm{\&mu;}}{\mathrm{\&sigma;}})$

$=\mathrm{\&Phi;}\left(\frac{a-\mathrm{\&mu;}}{\mathrm{\&sigma;}}\right)-\mathrm{\&Phi;}\left(\frac{b-\mathrm{\&mu;}}{\mathrm{\&sigma;}}\right)$

Here Z=(X-μ)/σ is for obeying a random element of standardized normal distribution, and Ф (Z) expression is positioned at the area that the standard normal density of Z left is covered, and this area is provided by gaussian distribution table, that is:

$\mathrm{\&Phi;}\left(z\right)={\&Integral;}_{-\&infin;}^{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">z</figure-callout>}}\frac{1}{\sqrt{2\mathrm{\&pi;}}}{e}^{-{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}^2/2}\mathrm{dt}$

Standard normal density

Modal statistical study incident is in design, and plural random element in overall is mutually comprehensive in the mode of certain regulation.At the determinacy mounting technology, often relate to be the assembling parts tolerance comprehensive with linear mode, that is:

X _Assembling=a ₁X ₁+ a ₂X ₂+ ...+a _nX _n

Usually, coefficient a _i=1 or a _i=-1, this depends on the action direction of i element in the tolerance chain.After plural overall random element is comprehensive with linear mode, then obtain one new overall, its average and variance are:

μ _Assembling=a ₁μ ₁+ a ₂μ ₂+ ...+a _nμ _n

And

$={\mathrm{\&sigma;}}_1^2+{\mathrm{\&sigma;}}_2^2+...+{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">n</figure-callout>}}^2$

To all i values if a ² _i=1, just draw the simplified style of top second formula, last standard deviation is σ ² _AssemblingSquare root.

Statistical tolerance determines that method generally is based on these points hypothesis:

The deviation Normal Distribution of-element size.

-production process is to add up (all deviations all occur at random) of control

-operation width (Process Spread) equals+/-3 σ, i.e. 6 σ.

For normal distribution on the whole, the parts of processing have 99.73% will fall in the operation width.

Statistics Working Procedure Controlling (SPC) is monitored manufacture process, the standardized technology that Working Procedure Controlling and process capability are confirmed.For determining whether operation is " competent ", must the research certain methods whether excessive with calculation deviation, or the operation average whether to depart from nominal value too far away.

In case determined the specification limit of parts and the inherent variability of operation, available following formula comes calculation process capacity factor C _p

Wherein USL and LSL are respectively the upper and lower specification limit.At technological capacity coefficient C _pIn, suppose the measured value Normal Distribution, but do not consider data that it only is the ratio of margin tolerance and process capability with respect to the concentrating of desired value.

Process capability index C _PkIt is the standard method of in a perdurability section, the process capability with statistics control characteristic being measured.C _PkIt is a reliable sign amount of operation performance.Consider the operation change

Deviation with relative nominal value

C _PkAvailable following formula calculates:

$\mathrm{Cpk}=\frac{\mathrm{USL}-\stackrel{\&OverBar;}{X}}{3\mathrm{\&sigma;}}$ With

In minimum value

For determining that whether a certain operation is statistics control operation, need fully measure, thereby can both characterize all possible source book or deviation.In arbitrary given time period,, think that then operation has the statistics control characteristic if all points all drop in the control limit (+/-3 σ).

If operation concentrates in the specification limit, then C _p=C _PkWhat express down is to different C _pValue, C _PkCorresponding working procedures percentage of failures (percent process fallout) when skew is arranged.This table has been considered the skew at operation and specification limit center.For reducing the number of defective part, can make operation concentrate with and/or reduce deviation.

To different C _pValue, C _PkCorresponding working procedures percentage of failures when skew is arranged

????Cp	???????????C pkSkew (Cp-Cpk)
				????0.00	????0.20	????0.40
	????.50	????13.361	????20.193				????38.556
????1.00				????.?270	????.836	????3.594
	????1.20	????.0318	????.1363				????.8198
????1.40				????.?0027	????.?0160	????.1350

In the determinacy assembling, the TOLERANCE ANALYSIS method has following three kinds.

1. the worst event method (arithmetic method)

2. model analysis

3. revise root sum of squares approach (RSS)

Concerning each method, it all is the same that the data of parts are selected with the tolerance integrated approach, and different is how the deviation of parts to be handled in analysis.

The worst affair analytical method is to understand easily, and it just contributes the arithmetic sum of item to calculate to each tolerance of build-up tolerance group.This is a kind of conservative approach, and in theory, if all parts can be manufactured in the specification limit, assembly parts will drop in the margin tolerance, so need not understand the situation of relevant each parts deviation profile.This analytical approach is the simplest.Consider that from making angle this method is ideal, because it need not understand the deviation of parts.If the tolerance of utilizing the worst event methods to calculate be can realize and can obtain qualified assembly parts, then these tolerances can adopt.

Some TOLERANCE ANALYSIS softwares have been arranged, and their adopt statistical simulation technology to predict because of design tolerance, instrument tolerance and manufacturing/assembling deviation and departure that assembly parts are produced.Some software can determine to estimate the main contribution factor and the contribution rate of deviation.

At first the mathematical model from assembly parts begins to simulate, normally with the input as model of the data of computer-aided design system.This model comprises the parts geometric configuration, tolerance change (design and operation) and assemble sequence.Utilize this model to simulate to the assembly parts of specified quantity, during simulation, in the margin tolerance and statistical distribution of regulation, the part that change is randomly assembled and the size of assembling jig.The output characteristics self-chambering accessory of being paid close attention to records, and with statistical method the result is analyzed.

Can provide the number percent of overproof assembly parts by statistical study.Utilize analogy method to determine to cause the main parts size of this deviation then.Can proofread and correct the problem that occurs, and it is incorporated in the model.And can adopt other analogy method to determine the validity of solution.

The three-dimensional simulation program will be by the personnel that pass through specialized training at the enterprising line operate of specialized equipment.It mainly is limited to labyrinth or easily changes the zone analyzes.And adopt other simple method that they are analyzed is difficult.

Carry out TOLERANCE ANALYSIS with the RSS method and be based on following hypothesis, promptly tolerance is comprehensive with linear mode.6 σ that traditionally whole tolerance range are decided to be the parts process capability doubly, thereby tolerance range available standards deviation is represented.

±t _detall＝±3σ _detall

$\&PlusMinus;{\mathrm{\&sigma;}}_{\det \mathrm{all}}=\frac{{\&PlusMinus;t}_{\det \mathrm{all}}}{3}$

When in the above normal distribution being discussed, notice, comprehensive for linearity

X _Assembling=a ₁X ₁+ a ₂X ₂+ ...+a _nX _n

Have

Thereby

$=\frac{1}{3}\sqrt{a_1^2{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_1^2+a_2^2{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_2^2}$

So

Here it is famous root quadratic sum (RSS) formula, or claim the statistical tolerance aggregative formula.

Know, utilize the RSS method to carry out TOLERANCE ANALYSIS, help making the tolerance range of parts to be relaxed, but on the low side to the estimation of assembly parts change.Therefore need a kind of method of determining effective element size tolerance limit for a long time, particularly in the operation of this important procedure parameter of part mean shift amount that causes limited size, for the large scale flexible assembly part that is assembled into by described parts, utilize the method accurately to estimate to the acceptable economically degree of its inconsistency.

One of purpose of the present invention provides a kind of improved method of determining effective element size tolerance limit, for the large scale flexible assembly part of making by described part, as the aircraft structure, utilize the method or to cooperate inconsistent degree accurately to estimate to its acceptable economically size.Another object of the present invention provides and a kind ofly improvedly is assembled into the method for large-scale flexible structure by many parts, though some parts is flexible, they still are in the set preload force limit of part.A further object of the present invention provides a kind of improved large scale flexible assembly part, it has one group of predetermined dimensional tolerence, these assembly parts are assembled by many parts, each parts has one group of component tolerances, with compare with traditional " the worst event methods " definite tolerance, described component tolerances is obviously relaxed.A further object of the invention provides a kind of method, it helps producing improved airplane component, these parts be drilled with the hole in advance and trim, replaceable airplane component constructed in accordance, thereby need not back drill (back drilling), cushioning or finishing also can make parts cooperate and make the hole alignment.Another purpose of the present invention is under the situation of the inconsistent pre-appraisal that does not increase assembly parts, to be based upon the increase and the parts C of mean shift amount in the parts manufacturing _PkThe gain and loss relation that value increases.

The many purposes of the present invention are to be realized by following method, promptly determine a kind of effective element size tolerance limit, utilize the method accurately to estimate the acceptable economically inconsistent degree of being made by described parts of large scale flexible assembly part, it comprises: the dimensional tolerence of determining assembly parts; The dimensional tolerence of assembly parts is distributed to its all parts to set up the single order estimator of component tolerances.Select a kind of preferred assemble sequence, in order to described parts are assembled into assembly parts, comprise reliable parts manufacturing process, and it is carried out validation.Suppose that tolerance is comprehensive with the worst event mode hardly; Make assembly parts have acceptable economically inconsistent rate, compare with the financial cost of the component tolerances institute manufactured parts of determining by the worst event methods, the former is favourable, therefore compares with the tolerance that obtains with the worst event methods, and element size tolerance limit of the present invention is relaxed.

Read following description of preferred embodiments by the reference accompanying drawing, will be better understood the present invention with and purpose, advantage.

Fig. 1 show a normal distribution overall in the distribution plan of parts measured value, and show deviation and be ± 1 σ, shared overall ratio when ± 2 σ and ± 3 σ.

Fig. 2 shows the center normal distribution, and mean shift is 10% o'clock distribution situation, their C _Pk=1.0.

Fig. 3 is C _Pk=1.0 o'clock, two kinds of distributions of working procedure parameter value showed the relation with the tolerance limit of being determined by the worst traditional event methods.

Shown in Fig. 4 is C along with processing parts _PkIncrease the gain and loss relation that is allowed between it and mean shift amount.

Shown in Fig. 5 is mean shift curve for one group of preliminary election, along with C _PkIncrease, the gain and loss relation between it and additional mean shift amount.

Fig. 6 shows according to tolerance evaluation process of the present invention.

Fig. 7 and 8 shows the tolerance range that calculates with assembling analytical approach of the present invention.

Among Fig. 9, fail in part drawing, correctly to mark with the determinacy assembly parts bilateral tolerance that statistical method derives.

Figure 10 A and 10B are cross-sectional view, and what illustrate is after provisional blind rivet is installed, the situation that part aligns and do not align.

Shown in Figure 11 to 13 is the example of pattern and pattern mark, is used for indicating the statistics requirement when using according to statistical tolerance of the present invention.

Figure 14 shows the overlapping situation that interference piece distributes.

Shown in Figure 15 to 17 is that drawing according to Figure 11 to 13 requires method that parts characteristic dimension measured value is assessed.

In the RSS method of the unmodified of prior art, suppose that operation concentrates on nominal value, and C _p=1.0, but because of being difficult to realize that the operation average does not always concentrate on nominal value, sees Fig. 2.Fig. 3 shows two kinds of possible parts and distributes C _Pk=1.0.For seven identical component tolerances chains of tolerance, set up the specification limit with traditional RSS method.As can be seen, for C _p=1.61; C _PkA distribution of=1.0 because the mean shift amount is very big, has the parts of half to exceed the limit deviation that obtains with the worst affair analytical method.The C that distributes _pBe worth greatly more, the parts that exceed the limit deviation that draws with the worst affair analytical method of arithmetic are many more.Because mean shift makes normal curve be offset towards an end of assembly parts design tolerance, has increased the inconsistent risk of assembly parts.For solving the mean shift of certain certain value effectively, can adopt expansion coefficient, promptly

The subscript Δ is represented " mean shift expansion ".In the past, correction factor M (n) only is used to adjust nonnormal central distribution, wherein M (n)＞1.Because this coefficient narrows down tolerance, thereby mean shift is had compensating action.But this fuzzy reasoning is not only at mean shift, specifically, is not only at allowing the mean shift amount.If the mean shift data of the process capability of parts and distribution are known, can determine the tolerance of parts more accurately.

To derive to correction factor M (n) below.When the assembly parts that formed by the determinacy assembly process were analyzed, it was suitable adopting the RSS method of revising.

Use following supposition in the analysis of assembly parts:

1. during modeling, all tolerances contribution Xiang Jun include by normal distribution:

The position in-hole

-material thickness

The gap in-fixture/hole

-flange gradient

2. all are contributed item with component number according to relevant tolerance, all parts mean shift amount must be controlled in the predetermined percentage of whole tolerance range.

3. the tolerance of parts is to be based upon on the selection of preferred manufacturing process of known capabilities, and the ability of this operation is represented with standard SPC Capability index.

4. the instrument tolerance is handled by the worst event methods.

Although the incomplete Normal Distribution of the measured value of parts characteristic dimension, in fact, they are all near normal distribution, and this is enough concerning the discussion of this paper.

As mentioned above, in the RSS method, suppose that an operation concentrates on a nominal value.But the parts characteristic dimension can depart from nominal value one in a small amount.Should be noted that concerning with the tolerance dimension of statistical method control, the drawing nominal size should appear at the center of tolerance range.Suppose that side-play amount and operation inherent variability are directly proportional.At present, be incomplete to process capability and the relevant understanding that makes operation concentrate on the ability of nominal value, must make hypothesis to available manufacturing capacity data.Just present understanding to process capability, the mean shift amount of the bearing accuracy of the mating holes of determinacy assembling is controlled at 10% of specification tolerance range to be considered to realize with interior, this inclined to one side weighing can be used as the preliminary election side-play amount, is used for the assembling inconsistency that described mating holes causes is estimated.Can select other skew controlled quentity controlled variable according to manufacturing capacity known or expectation.

Still it is comprehensive to adopt the RSS method to carry out tolerance.Available two kinds of methods are derived to correction factor M (n).In first method, mean shift comprehensively is limited in it in above-mentioned 10% by algorithmic approach or the worst event methods, and combines with it with by other deviation of RSS method synthesis.In the second approach, regard mean shift as random quantity, use the RSS method, mean shift is comprehensive, it is limited in 10%, and with algorithmic approach it and other deviation with the RSS method synthesis is added and to be in the same place.

In first method, the mean shift of assembly parts is retrained by the mean shift by the comprehensive element size of the worst event methods.The average of i part and nominal value are respectively by μ _iAnd υ _iDetermine Δ=μ _i-υ _iRepresent corresponding mean shift, then the mean shift of assembly parts is retrained by following formula:

| μ _Assembling-ν _Assembling|=| a ₁Δ ₁+ ...+a _nΔ _n|

≤|a ₁||Δ ₁|+...+|a _n||Δ _n|

=η ₁| a ₁| t ₁+ ...+η _n| a _n| t _nHere η _i=| Δ _i|/t _iExpression mean shift amount and part tolerance t _iBe directly proportional.Because mean shift will be limited in 10%, promptly | Δ _i|/(2t _i)≤0.10 requires η to all parts _i≤ 0.20, the absolute mean side-play amount of given parts | Δ _i| and C _Pk〉=1.0, the maximum value that can draw the standard deviation of parts is

${\mathrm{\&sigma;}}_i\&le;\frac{t_i-\left|{\mathrm{\&Delta;}}_i\right|}{3}=\frac{t_i-{\mathrm{\&eta;}}_i{t}_i}{3}=\frac{t_i(1-{\mathrm{\&eta;}}_i)}{3}$

So the maximum value of the standard deviation of assembly parts is

To carry out this upper limit that deviation comprehensively draws and the mean shift amount integrated value η that obtains with the worst event methods with the RSS method ₁| a ₁| t ₁+ ...+η _n| a _n| t _nWith algorithmic approach or the worst event methods addition, can draw

$\&le;927\sqrt{[a_1{t}_1(1-{\mathrm{\&eta;}}_1){]}^2+...+[a_n{t}_n(1-{\mathrm{\&eta;}}_n){]}^2}+{\mathrm{\&eta;}}_1\left|a_1\right|{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_1+...+{\mathrm{\&eta;}}_n\left|a_n\right|t_n,$

.927=2782/3. wherein

RSS deviation integrated value is got 2.782 σ in the formula _Assembling, rather than 3 σ _Assembling, this is because have only the one-sided afterbody of normal distribution can cause and build-up tolerance ± T _{1, assembling}Inconsistent risk is arranged.In traditional center RSS analytical approach, this risk probability is 0.0027.To standardized normal distribution, the probability above 2.782 is 0.0027.

To η _i≤ η ₀=0.20 works as η ₁=...=η _n=η ₀The time, T _{1, assembling}The upper limit reach maximal value.Use T _{1, assembling}Make the upper limit and will form maximum (guarding) build-up tolerance

At equal tolerance contribution item | a ₁| t ₁=...=| a _n| t _nThe time, utilize the worst event methods, can further determine the tolerance limit of assembly parts,

Wherein

In the comprehensive second method of mean shift amount, suppose that each mean shift produces at random, thereby utilize them to carry out RSS when comprehensive that the result will eliminate some deviations.If mean shift is disposable at random, promptly a random quantity only produces once in an accessory size operation, then the mean shift Δ _i=μ _i-υ _iCan regard as is from interval [η ₀t _i, η ₀t _i] in randomly draw.It also can be expressed as

Δ _i=η ₀t _iY _iY wherein _iGo up to evenly distributing in interval [1,1].In case obtain these mean shift amounts at random, by satisfying C _Pk〉=1.0 requirement can limit parts characteristic dimension deviation, promptly

${\mathrm{\&sigma;}}_i\left(Y_i\right)\&le;\frac{t_i-\left|{\mathrm{\&Delta;}}_i\right|}{3}=\frac{t_i(1-|Y_i\left|{\mathrm{\&eta;}}_0\right)}{3}$

The deviation of assembly parts and nominal value can be write:

X _Assembling-ν _Assembling=a ₁(X ₁-ν ₁)+...+a _n(X _n-ν _n)

＝a ₁(X ₁-μ ₁)+...+a _n(X _n-μ _n)+a ₁(μ ₁-ν ₁)+...+a _n(μ _n-ν _n)

To determining the fixed value Y=(Y of each parts mean shift amount ₁..., Y _n), can be with assembly parts deviation X _Assembling-υ _AssemblingBe similar to and regard normal distribution as, its average and variance are:

μ _Assembling(Y)=a ₁(μ ₁-ν ₁)+...+a _n(μ _n-ν _n)

＝a ₁η ₀t ₁Y ₁+...+a _nη ₀t _nY _n

$\&le;a_1^2\frac{{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_1^2{(1-|{\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1\left|{\mathrm{\&eta;}}_0\right)}^2}{3^2}+...+a_n^2\frac{t_n^2{(1-|Y_n\left|{\mathrm{\&eta;}}_0\right)}^2}{3^2}$

Notice X _Assembling-υ _AssemblingAverage and variance relevant by the main and resulting mean shift of Y.For fixing Y, can expect X _Assembling-υ _AssemblingIn have 99.3% value to fall into

μ _Assembling(Y) ± 3 σ _Assembling(Y)

When the Y value changes, this interval will nearby change.Each group is sent into the operation of parts of the assembling of a certain type, the above-mentioned value Y of decision mean bias only occurs once.For nearly all available Y value, above-mentioned interval is contained in available one bigger interval [A, B], promptly has big probability, gets here and does 0.9973, can obtain

P (is included in [A, B] interval interior [μ _Assembling(Y)-3 σ _Assembling(Y), μ _Assembling(Y)+3 σ _Assembling(Y)])=0.9973.

The actual value of A and B is calculated below, they and [μ _Assembling(Y)-3 σ _Assembling(Y), μ _Assembling(Y)+3 σ _Assembling(Y)] actual value difference, because in the design phase, available actual mean shift amount and Y ₁Be not known prior imformation, the latter is unknown.That use in the build-up tolerance interval is interval [A, B], at all assembling deviation X _Assembling-υ _AssemblingIn have at least 99.73% to fall into this interval.

Obtain after all parts operation mean shift amounts, consider that the assembly parts that much ratios are arranged drop on outside [A, B] interval

I (Y)=[μ _Assembling(Y)-3 σ _Assembling(Y), μ _Assembling(Y)+3 σ _Assembling(Y)]

Caught the normal density of its both sides, center 99.73%.Normal density is at this interval [A, B] when going up move left and right, if this interval I (Y) is near A or B, then the area that normal density covered outside [A, B] reaches maximal value, at this moment, the one-sided meeting of having only normal density is to falling into [A, B] outside probability exert an influence, this probability has only half of original probability 0.0027, promptly is about 0.00135.For this is revised, make

I (Y)=[μ _Assembling(Y)-2.782 σ _Assembling(Y), μ _Assembling(Y)+2.782 σ _Assembling(Y)]

When promptly defining I (Y), coefficient is got and is done 2.782, rather than 3, because of P (Z＞2.782)=1-Ф (2.782)=0.0027.This makes that falling into tolerance interval [A, B] assembly parts in addition mostly is most 0.27%.Owing to do not know the position of interval I (Y) in [A, B], so used determiner " at most ".

Also need seek bigger closed interval [A, B], when definite I (Y) is interval, allow Y probability of occurrence deviation.The upper limit or the lower limit of I (Y) can exceed [A, B], i.e. μ _Assembling(Y)+2.782 σ _Assembling(Y)＞B, or μ _Assembling(Y)-2.782 σ _Assembling(Y)＜A.If this risk probability classifies 0.0135 as, then the probability that falls into outside [A, B] of the interval end points of I (Y) is 0.00135+0.00135=0.0027, and containing probability then is its complementary, promptly desirable 0.9973.

Be that probability with 0.99865=1-0.00135 retrains μ by B above _Assembling(Y)+2.782 σ _Assembling(Y), but to interval endpoint with

It is more favourable retraining, that is:

$\&le;{\mathrm{\&eta;}}_0[w_1{\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1+...{+w}_n{Y}_n]+\frac{2782}{3}\sqrt{{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">w</figure-callout>}}_1^2{(1-|{\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1\left|{\mathrm{\&eta;}}_0\right)}^2+...+w_n^2{(1-|Y_n\left|{\mathrm{\&eta;}}_0\right)}^2}=B\left(Y\right)$

W wherein _i=a _it _i/ T ^* _AssemblingBecause Y is a random quantity, the normal distribution of upper limit B (Y) approximate quantity.N 〉=5 o'clock, approximation is fine.2≤n≤4 o'clock, the build-up tolerance limit that obtains is guarded.In addition, verified, when tolerance contribution item equates, promptly | a ₁| t ₁=...=| a _n| t _nOr ${\mathrm{<figure-callout\; id="1"\; label="W"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">W</figure-callout>}}_1=...=W_n=1/\sqrt{n}$ The time, the build-up tolerance limit is the most conservative.To second kind of situation, normal distribution average and the standard deviation of upper limit B (Y) are:

${\mathrm{\&mu;}}_F=\frac{2782}{3}\sqrt{1-{\mathrm{\&eta;}}_0+{\mathrm{\&eta;}}_0^2/3}=.927\sqrt{1-{\mathrm{\&eta;}}_0+{\mathrm{\&eta;}}_0^2/3}=.83632$ To η ₀=.2

${\mathrm{\&sigma;}}_F=\frac{{\mathrm{\&eta;}}_0}{\sqrt{3}}=.1155$ To η ₀=.2

Like this

P(B(Y)≤μ _F+3σ _F)＝Ф(3)＝.99865.

Get

Following formula is set up for 99.865% of all Y or mean shift possibility, thereby

Probability is 0.00135, and is same,

$\&GreaterEqual;{\mathrm{\&eta;}}_0[w_1{\mathrm{<figure-callout\; id="1"\; label="Y"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">Y</figure-callout>}}_1+...+w_n{Y}_n]-\frac{2782}{3}\sqrt{{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">w</figure-callout>}}_1^2{(1-|{\mathrm{<figure-callout\; id="0"\; label="Y"\; filenames="A20041000536100321.png"\; state="\{\{state\}\}">Y</figure-callout>}}_0\left|{\mathrm{\&eta;}}_0\right)}^2+...+w_n^2{(1-|Y_n\left|{\mathrm{\&eta;}}_0\right)}^2}=A\left(Y\right)$

Wherein A (Y) is approximately normal distribution, and its average is-μ _F, standard deviation is σ _FThereby:

P(A(Y)≥-μ _F-3σ _F)＝1-Ф(-3)＝Ф(3)＝0.99865

Get A _F=-B _F, A=A _FT ^* _Assembling=-B

For 99.865% of all Y or mean shift possibility

μ _Assembling(Y)-2.782 σ _Assembling(Y) 〉=A=A _FT ^* _Assembling, thereby

μ _Assembling(Y)-2.782 σ _Assembling(Y)＜A (η ₀=0.2 o'clock, A=-1.183T ^* _Assembling)

Its probability is 0.00135.Therefore, the probability that I (Y) exceeds outside [A, B] is 0.00135+0.00135=0.0027, and the probability that is included in the mean shift in [A, B] is a complementary 99.73%.

Because-A=B, the intermediate value of closed interval [A, B] is zero.Be source and and the T that emphasizes tolerance _{1, assembling}In the different in kind of mean shift arithmetic integrated approach, B and-A all uses T _{2, assembling}Expression.

Thereby after other deviation and circulation deviation of the deviation of considering with statistical method the disposable mean shift when comprehensive and parts characteristic dimension, build-up tolerance is pressed the following formula constraint

Wherein

$M_2\left(n\right)=B_F=.927\sqrt{1-{\mathrm{\&eta;}}_0+{\mathrm{\&eta;}}_0^2/3}+{\mathrm{\&eta;}}_0\sqrt{3}(=1.183\mathrm{for}{\mathrm{\&eta;}}_0=.2).$

Note, and M ₁(n) contrast can be found out M ₂(n) irrelevant with n, this is that mean shift is by the comprehensive result of statistical method.

Heretofore when obtaining actual process number and confirm the statistical property of pilot hole mean shift according to this, suppose that the actual correction coefficient just thinks reasonably between two kinds of methods.

As trading off of two kinds of methods, get M ₁(n) and M ₂(n) average is as correction factor:

$M\left(n\right)=\frac{M_1\left(n\right)+M_2\left(n\right)}{2}=\frac{(.927)(.8)+.2\sqrt{n}+1.183}{2}=\frac{1.925+.2\sqrt{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">n</figure-callout>}}}{2}$

Following table has provided different n values, M ₁(n), M ₂(n) and the value of average correction factor M (n).

????n	????2	????3	????4	????5	????6	????7	????8
								??M 1(n)	??1.024	??1.088	??1.142	??1.189	??1.231	??1.271	??1.307
??M 2(n)	??1.183	??1.183	??1.183	??1.183	??1.183	??1.183	??1.183
								??M(n)	??1.104	??1.136	??1.162	??1.186	??1.207	??1.227	??1.245

When research parts analytical approach, find in the body tolerance group of a typical aircraft that the number of main tolerance is about 8.For the tolerance group that 8 main tolerance contribution items are arranged, RSS correction factor M (n)=1.25 can be used as a kind of simple conservative method for the majority analysis.But, can use the coefficient in table and the above-mentioned formula if assemble sequence/processing scheme is verified.

From top discussion as can be seen, within the scope of the invention, for trying to achieve other RSS correction factor, preliminary election mean shift amount is not 10%.Under most occasions, 20% the preliminary election mean shift limit is the practical limit, because of the skew limit is big more, just approaches the worst incident tolerance limit more, the benefit of the part tolerance of broad when having reduced to use statistical method to determine tolerance.

Because can find the preferred parts manufacturing process above the preliminary election mean shift limit, people are desirable to provide a kind of parts acceptance method, the assembly parts for making according to the initial mean shift limit utilize the method can not increase the risk probability of assembly parts.

Mean shift can have a negative impact to the comprehensive the worst incident aspect of tolerance after increasing.Can prove, to a certain extent, when the increase of preliminary election part mean shift surpasses 10%, the reduction (C of part deviation _PkIncrease) compensation to mean shift is acceptable.Establish the specification limit of assembly parts and selected the initial mean shift limit, and after distributing tolerance for each parts by above-mentioned steps, just obtained C _PkAnd the balance method between the mean shift that increases.In order to make the gain and loss balance relation between the part uncorrelated mutually, in described comprehensive step, adopt the worst event scheme, that is, make the mean shift of all parts all be increased to identical number percent (being higher than 10%), and make C _PkSuitably increase to a certain identical value C _PkThereby＞1.0 compensate mean shift.This gain and loss relation of below will deriving.

Partly use η from i the observed new maximum mean shift of parts operation ^*Expression, that is, | μ _i-υ _i|≤η ^*t _i=(η ^*/ 2) 2t _iCorrespondingly, the C that this mean shift is compensated _PkUse C ^* _PkExpression.When beginning to set forth tolerance and determine method, all parts operations are all supposed C _Pk＞1.0.Wish C herein much larger than 1.0 _PkiBe enough to compensation than preferred value η ₀Value η after=0.2 (mean shift 10%) increases ^*Tight root be derivation to M (n), still continue to use identical symbol,

${\mathrm{Cpk}}_i=\frac{t_i(1-{\mathrm{\&eta;}}_i)}{{3\mathrm{\&sigma;}}_i}\&GreaterEqual;{\mathrm{Cpk}}^{*}\&DoubleRightArrow;{\mathrm{\&sigma;}}_i\&le;\frac{t_i(1-{\mathrm{\&eta;}}_i)}{3{\mathrm{Cpk}}^{*}}$

So C _Pk ^*Big more, just mean that deviation is more little, i.e. σ ₁More little, can obtain assembling standard deviation thus

$\&le;\sqrt{[a_1{t}_1(1-{\mathrm{\&eta;}}_1)/\left({3\mathrm{Cpk}}^{*}\right){]}^2+...+[a_n{t}_n(1-{\mathrm{\&eta;}}_0)/\left({3\mathrm{Cpk}}^{*}\right){]}^2}$

With 2.782 σ _AssemblingWith with the comprehensive mean shift η of the worst event methods ₁| a ₁| t ₁+ ...+η _n| a _n| t _nWith the worst event mode addition, obtain

$=.927\sqrt{[a_1{t}_1(1-{\mathrm{\&eta;}}_1){]}^2+...+[a_n{t}_n(1-{\mathrm{\&eta;}}_n){]}^2}+{\mathrm{\&eta;}}_1\left|a_1\right|{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_1+...+{\mathrm{\&eta;}}_n\left|a_n\right|t_n$

η wherein _i≤ η ^*, work as η ₁=...=η _n=η ^*The time, η _iReach maximum value.As before, following formula can be reduced to

Wherein ${\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">M</figure-callout>}}_1^{*}\left(n\right)=\frac{.927(1-{\mathrm{\&eta;}}^{*})}{\mathrm{Cp}{k}^{*}}+{\mathrm{\&eta;}}^{*}\sqrt{n}$ and

Be assumed to the worst incident that equates tolerance contribution item, promptly | a ₁| t ₁=...=| a _n| t _n

In the other method of research mean shift, also be to adopt the statistical tolerance method to determine mean shift, be about to the mean shift Δ _iRegard random quantity as, Δ _i=η ^*t _iy _i, supposition here becomes Y at random _iOn [1,1] interval, evenly distribute.According to the derivation of front, but introduce more harsh C _PkValue can draw

Wherein

${\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">M</figure-callout>}}_2^{*}\left(n\right)=\frac{.927}{{\mathrm{Cpk}}^{*}}\sqrt{1-{\mathrm{\&eta;}}^{*}+{\mathrm{\&eta;}}^{*2}/3}+\sqrt{3}{\mathrm{\&eta;}}^{*}.$

With the front to two kinds of methods carry out compromise corresponding, the mean value of desirable two expansion coefficient,

$M^{*}\left(n\right)=\frac{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">M</figure-callout>}}_1^{*}\left(n\right)+{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">M</figure-callout>}}_2^{*}\left(n\right)}{2}$

$=\frac{.927}{{\mathrm{Cpk}}^{*}}\frac{1-{\mathrm{\&eta;}}^{*}+\sqrt{{1-\mathrm{\&eta;}}^{*}+{\mathrm{\&eta;}}^{*2}/3}}{2}+{\mathrm{\&eta;}}^{*}\frac{\sqrt{n}+\sqrt{3}}{2}.$

For the risk probability that makes assembly parts with M (n) T ^* _AssemblingBe in same level as the resulting risk probability of the comprehensive amount of build-up tolerance, should make

Perhaps, for η ₀=0.2 o'clock

$.927\frac{1-{\mathrm{\&eta;}}_0+\sqrt{1-{\mathrm{\&eta;}}_0+{\mathrm{\&eta;}}_0^2/3}}{2}+{\mathrm{\&eta;}}_0\frac{\sqrt{n}+\sqrt{3}}{2}=.962+.1\sqrt{n}$

$=\frac{.927}{{\mathrm{Cpk}}^{*}}\frac{1-{\mathrm{\&eta;}}^{*}+\sqrt{1-{\mathrm{\&eta;}}^{*}+{\mathrm{\&eta;}}^{*2}/3}}{2}+{\mathrm{\&eta;}}^{*}\frac{\sqrt{n}+\sqrt{3}}{2}$

Thereby can obtain C _Pk ^*And η ^*Between gain and loss relation:

${\mathrm{Cpk}}^{*}=\frac{.927(1-{\mathrm{\&eta;}}^{*}+\sqrt{1-{\mathrm{\&eta;}}^{*}+{\mathrm{\&eta;}}^{*2}/3})}{1.924+.2\sqrt{n}-{\mathrm{\&eta;}}^{*}(\sqrt{n}+\sqrt{3})}.$

Fig. 4 shows in described assembling, for the amount of parts n of different assembly parts, C ^* _PkAnd η ^*Gain and loss relation.To initial value η ₀, gain and loss is closed and is:

${\mathrm{Cpk}}^{*}=\frac{.927(1-{\mathrm{\&eta;}}^{*}+\sqrt{1-{\mathrm{\&eta;}}^{*}+{\mathrm{\&eta;}}^{*2}/3})}{.927(1-{\mathrm{\&eta;}}_0+\sqrt{1-{\mathrm{\&eta;}}_0+{\mathrm{\&eta;}}_0^2/3})+({\mathrm{\&eta;}}_0-{\mathrm{\&eta;}}^{*})(\sqrt{n}+\sqrt{3})}$

For different preliminary election mean shift amount η ₀, when n=8, second kind of gain and loss relation illustrated by Fig. 5.

As shown in Figure 6, according to the present invention, the first step of tolerance evaluation process is to determine to satisfy the required final assembly parts tolerance of functional matching requirements.When showing on stabilized polyester (stablemylar) drawing that with traditional method for designing installation concerns, in most characteristic dimension tolerances of commercial transport are defined in mutually ± 0.03, and utilize frock to satisfy this requirement.In the past, the method for this distribution tolerance met the demands fully when manufacturing resembles the compliant mechanism of aircraft and so on, thereby it is by make the structure of the mutually positioning establishment of parts assembly parts with the rigidity frock.Yet, adopt determinacy to assemble this manufacturing technology, frock can be simplified greatly, even can cancel.Owing to when making position components, no longer need frock, before distribution is assessed to component tolerances, must establish the tolerance dimension at the mating surface place of assembly parts.

When utilizing the such new technology of determinacy assembling to assemble said structure, do not need frock, just, the parts of being installed are deformed in preloading the limit, until the relation between fit dimension is set up the part location.For example the mating holes on two parts is aimed at.Therefore be the qualification rate of determining build-up tolerance, in TOLERANCE ANALYSIS, must consider the part deflection and the unrelieved stress that produce because be out of shape (Pull-down) by force.For bearing parts big load and that be easy to fatigue, this distortion by force is unallowed.When determining the tolerance of qualified assembly parts, must consider following factor, but be not limited only to these factors.

Ideal relationship between the-counterpart

The desired how much assembling standards of-do as one likes energy or profile

-minimum/maximal clearance

-distortion/cushioning requirement by force.

Be the assembling deviation that calculates to a nicety, must determine the operation of each concrete parts.Preferred parts manufacturing process determines by the most reliable and the most economic manufacturing process is unique.Selected operation must be " competent ".Process variable to the influence of finished part by the manufacturing capacity quantitative description.Process variable comprises: environment and device temperature, equipment rigidity, periodicity maintainability, material deviation, feeding and cutting speed, cutting fluid state, cutter sharpness etc.

Carry out before the determinacy assembly tolerance analysis, must be to component number according to selecting.Want correctly to select these data, essential tolerance and the parts fabrication scheme of understanding final assembly parts.When assembling is analyzed, with the build-up tolerance budget allocation to each parts, must identify the actual characteristic size of parts.Analyze based on assembling, in order to represent the deviation of parts exactly, design must be consistent with selected data with processing.

Adopt improved RSS analytical approach can to along coordinate system each coordinate X, Y, the deviation of Z direction estimate respectively.For determining the build-up tolerance route, must be clearly shown that X, Y, the Z reference frame of assembling analysis usefulness.Do not have reference frame, it is meaningless that tolerance value will become.

Although can analyze separately the tolerance of two different directions of mating holes, this both direction usually must satisfy different tolerances.After having determined the maximum constraints statistical tolerance, the drawing tolerance is pressed mark shown in Fig. 7,8.

Said method and physical dimension mark and tolerance are calculated (GD﹠amp; T) used empirical method difference in.At GD﹠amp; In the T method, total fit tolerance zone be multiply by 1.4, just foursquare tolerance range can be converted to circular physical location tolerance range.If in design, consider the interchangeability of securing member, be beneficial to GD﹠amp; The T method can allow pilot hole that extra manufacturing tolerance is arranged.In the determinacy assembly method, do not consider securing member interchangeability usually, but consider the position of related features of parts that this position of related features is connected by the pin between the Kong Yukong to be controlled.For example

t _x＝±0.010????t _y＝±0.007

If being pressed rectangular tolerance zone, each tolerance handles the diameter 0.0244 of the physical location tolerance range that then obtains.GD﹠amp as shown in Figure 9; T drawings marked method is incorrect, if be labeled as φ 0.0244 on the drawing, then according to the requirement of part drawing, it is qualified that whole shadow regions are all thought.But all parts that drop within the shadow region have all exceeded the margin tolerance that calculates with statistical method, thereby overproof assembly parts number has increased.In some cases, may be better than manufacturing capacity along the manufacturing capacity of a certain change in coordinate axis direction along another change in coordinate axis direction.If TOLERANCE ANALYSIS result allows, can on drawing, mark rectangular tolerance zone, can avoid like this because of using standard GD﹠amp; T term and the misunderstanding that may cause.

Because in the determinacy assembling, the build-up tolerance that securing member can seriously influence, therefore how the type of the securing member of assembly parts in must the understanding scheme also will be understood securing member and be and the cooperating of mating holes, to indicate the just size in included gap in the tolerance route.

Cleco and the provisional securing member of Wedgelock type provide very little mating holes self-centering.In addition, have only to produce radially and align along the normal direction of " bow (bow) " of securing member.

In many determinacy assembling occasions, adopt band to take out the blind rivet of core bar as provisional securing member.When final securing member was installed, the central openings of described provisional securing member was used for optical correction and provisional securing member is bored remove.

When blind rivet was installed, core bar expanded the main body of securing member.For light flexible spare, the alignment of when main body expands and hole, thus in TOLERANCE ANALYSIS, can consider the gap.When pts wt increase or rigidity increase, can overcome the self-centering effect of blind rivet, thereby self-centering can not take place.See Figure 10 A, 10B.

When determining the gap in hole, must consider the mating capability in securing member and concrete hole, this gap will join in the tolerance route.For example, if when securing member is installed in the hole of φ 0.1406-φ 0.1436, the following φ 0.136 that is limited to that selected securing member expands, then when assembly tolerance analysis, it is rational doing following consideration.

＝0.1421

T _{Blind rivet}=0.1421-0.136

＝ 0.0061

Above-mentioned tolerance is applied in the TOLERANCE ANALYSIS method,

As mentioned above, usually must rely on the expansion of provisional securing member and obtain required assembly precision.Expansion makes the hole align mutually, and the size of pore does not have much.At traditional GD﹠amp; In the T method, to mark the drawing tolerance in hole usually with materials behavior maximum modified amount (MMC).But the MMC correction can make assembly precision descend when adopting expansion fastener.In addition, when part is checked and accepted, use the MMC correction can make the evaluate complicatedization of statistics.Therefore, as follows, mark the drawing deviation (Callout) that derives by statistical method with extraneous features size (regardless of feature size (RFS)) correction.

When adopting determinacy assembly method and frock that parts are assembled, must when TOLERANCE ANALYSIS, consider the frock influence.For reducing the additional tolerance that frock is brought as much as possible, must predict the deviation on frock and part composition surface according to the characteristic dimension of determinacy assembly parts.Because the frock number generally seldom, its tolerance can not be by the normal distribution modeling.When TOLERANCE ANALYSIS, the tolerance of frock should be distributed by the worst incident point-score, as shown in the formula described, and outside comprehensive of frock tolerance Xiang Tizhi RSS,

When utilizing the RSS method of revising that build-up tolerance is assessed, some tolerance contribution items in the tolerance route are characteristic dimensions of parts, when determining the tolerance of these sizes, must not control mean shift, but, these characteristic dimensions are remained favourable by tolerance is carried out statistical treatment.One group of hole on the large aircraft skin panel is an example of such parts.Cooperate for making between the parts, these skin panels are controlled the relation between the parts, and are general and do not require with respect to component number and according to reference frame mean shift is controlled.To the position distribution in hole control be the design in main target.Therefore in TOLERANCE ANALYSIS, must identify these tolerance contribution items, and they are suitably handled.Comprised correction factor M (n) in analytical approach, this coefficient can exert an influence to all the tolerance contribution items in the quadratic sum root.M (n) be to the worst event methods and with statistical method to the mean shift amount average compromise after comprehensive.For purposes of illustration, suppose preceding two tolerances contribution t ₁And t ₂Not influenced by mean shift, and mean shift is to a n-2 remaining tolerance contribution t ₃... t _nThe generation effect.On the parts drawing, be with t ₁And t ₂Such tolerance item standard is come out, and sees Figure 11-13.

For other the mean shift situation or do not have the mean shift situation, can be out of shape following formula at an easy rate.The derivation to the worst incident mean shift integrated approach according to the front can draw

Capping is as T _{1, assembling}Final expression formula.Two zero-mean side-play amount contribution influences that produced are

$M_1\left(n\right)=0.927(1-{\mathrm{\&eta;}}_0)+{\mathrm{\&eta;}}_0\sqrt{n-2}$ In Replaced $M_1\left(n\right)=0.927(1-{\mathrm{\&eta;}}_0)+{\mathrm{\&eta;}}_0\sqrt{n}$ In

Similar with the derivation of mean shift statistics integrated approach, can obtain

$\&times;\sqrt{{(1-{\mathrm{\&eta;}}_0)}^2(a_1^2{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_1^2+a_2^2{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_2^2)+a_3^2{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="A20041000536100401.png"\; state="\{\{state\}\}">t</figure-callout>}}_3^2+...+a_n^2{\mathrm{<figure-callout\; id="2"\; label="t\; n"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_n^{}}.$

Wherein

$\tilde{R}={\tilde{w}}_3^2+...+{\tilde{w}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">n</figure-callout>}}^2$ Wherein ${\tilde{w}}_1^2=\frac{a_1^2{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_1^2}{{(1-{\mathrm{\&eta;}}_0)}^2(a_1^2{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_1^2+a_2^2{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_2^2)+a_3^2{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="A20041000536100401.png"\; state="\{\{state\}\}">t</figure-callout>}}_3^2+...+a_n^2{\mathrm{<figure-callout\; id="2"\; label="t\; n"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_n^{}}$

for?i＝3，...，n.

Be appreciated that in the derivation and former derivation herein each deviation t _i(i=1,2 ... be that 3 times of parts operation deviation multiply by expansion coefficient 1/ (1-η n) ₀) be t _i=3 σ _i/ (1-η ₀).

Because in these two kinds of methods, each in the root quadratic sum is incomplete same, thus just be not only the problem that multiple is averaged and traded off, and these two kinds of build-up tolerances on average should be traded off, promptly

This tolerance to no mean shift influence contributes the disposal route of item loaded down with trivial details a bit.Better simply aggregative formula carries out rationally that approximate (approximate error is T below available _Assembling10%), this is at existing two not provided by the situation K=2 of the tolerance that mean shift influences equally, this formula mainly is rule of thumb to set up with the RSS method of revising.

Wherein

$M\left(n\right)=\frac{.927(1-{\mathrm{\&eta;}}_0)+{\mathrm{\&eta;}}_0\sqrt{n}+.927\sqrt{1-{\mathrm{\&eta;}}_0+{\mathrm{\&eta;}}_0^2/3}+{\mathrm{\&eta;}}_0\sqrt{3}}{2}$

T ^* _AssemblingIn the formula, the purpose of the M under the radical sign in the denominator (n-2) is to eliminate the influence of the preceding expansion coefficient of radical sign.The factor (1-η in this radical sign ₀) ²Can make because of considering mean shift 1/ (the 1-η that expands ₀) doubly tolerance t ₁And t ₂Reduce.

Analyze calculating by RSS, can predict, have 0.27% assembly parts to exceed the tolerance limit of calculating build-up tolerance.The tolerance of assembling in scheme can not be divided timing by the RSS method, can think that still scheme is an acceptable, but condition is, to the allowable tolerance of the assembly parts made under the known manufacturing capacity, the inconsistency of the assembly parts of being predicted is still thought very little.

For parts that might interfere or assembly parts, we are interested to be to interfere probability.When the size of parts A (or assembly parts A) can interfere during greater than the size of parts B (or assembly parts B), see Figure 14.

With Ф (Z) calculating probability A-B＞0 (do not have and interfere), Ф is previously defined Standard Normal Distribution,

$Z=\frac{{\mathrm{\&mu;}}_A-{\mathrm{\&mu;}}_{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">B</figure-callout>}}}{\frac{1}{3}\sqrt{{\mathrm{<figure-callout\; id="2"\; label="t\; A"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_A^{}+{\mathrm{<figure-callout\; id="2"\; label="t\; B"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_B^{}}}.$

Generally, actual average μ _A, μ _BWith drawing nominal value υ _A, υ _BDifferent.The mode that people can produce mean shift with and control method make all hypothesis.Following short-cut method can be used to interfering probability to carry out conservative prediction, and inconsistent degree mostly is 0.27% most, and promptly calculating with following formula does not have the probability Ф (Z) of interference

$Z=\frac{{\mathrm{\&nu;}}_A-{\mathrm{\&nu;}}_B}{\frac{M\left(n\right)}{3}\sqrt{{\mathrm{<figure-callout\; id="2"\; label="t\; A"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_A^{}+{\mathrm{<figure-callout\; id="2"\; label="t\; B"\; filenames="A20041000536100401.png,A20041000536100411.png"\; state="\{\{state\}\}">t</figure-callout>}}_B^{}}}$

If do more complicated processing, the precision of prediction that inconsistency is surpassed 0.27% interference probability is improved.

Utilize GD﹠amp; The T method determines that tolerance can guarantee that the interchangeability of the securing member installed on the interworking parts reaches 100%:

T＝H-F

Wherein T is a tolerance,

H is the MMC hole

F is the MMC securing member

The RSS method of common available correction is analyzed the installation statistical forecast amount of securing member.For analyzing,, usually the composite elements tolerance chain that the flexible assembly part forms can be reduced to the linear tolerance route by ignoring along the error in the hole of deflection direction.The problem that can not cause securing member to install along the error of this direction, and this problem is at GD﹠amp; Think very important in the T TOLERANCE ANALYSIS equally.This problem usually runs in aircraft partial structurtes assembly parts, and this sub-assemblies has flexibility on both direction, when in the end assembling securing member is fixed thereon.

In case established effective build-up tolerance, and determined from considering acceptable parts process capability (C economically _Pk〉=1.0), just can analyze, distribute build-up tolerance to each parts on the assembly parts.In this analyzed, the assembling effect was to weigh according to the size that the parts average allows to depart from nominal size in preset range.Following formula is used for setting up the discrete tolerance of parts on the iteration basis, see Fig. 6.

Wherein

$M\left(n\right)=\frac{.927(1-{\mathrm{\&eta;}}_0)+{\mathrm{\&eta;}}_0\sqrt{n}+.927\sqrt{1-{\mathrm{\&eta;}}_0+{\mathrm{\&eta;}}_0^2/3}+{\mathrm{\&eta;}}_0\sqrt{3}}{2}$

t _iThe process capability tolerance limit of 〉=parts scheme operation, the C of this operation _PkBe at least 1.0.

If assembling the analysis showed that when parts adopted economic arithmetic tolerance, 100% assembly parts satisfied tolerance, then should mark traditional arithmetic tolerance on drawing according to suitable industrial standard such as ANSI-Y14.5.If component tolerances is than the expectation value harshness, if but still can realize, preferably both indicated traditional arithmetic tolerance, also mark statistical tolerance.

Similar to the drawings marked that the parts that satisfy matching requirements with traditional arithmetic tolerance or more loose statistical tolerance carry out with pattern shown in Figure 11.On parts list, should add following explanation.

Statistical tolerance characteristic dimension applied statistics Working Procedure Controlling method is made, or makes by illustrated more strict arithmetic tolerance.Have only when the operation measured value satisfies following the requirement, statistical tolerance is only suitable, 1) Working Procedure Controlling figure should show that relevant manufacture process is controlled.2) average is not more than 10% of specification tolerance to the skew of nominal value.3) C _PkBe at least 1.0, and 90% degree of confidence is arranged.

Have only in the time of to control the mean shift of parts characteristic dimension, just use above-mentioned explanation.

If only be met the component tolerances of matching requirements, on drawing, mark with the mode of similar Figure 12 with statistical analysis technique.In parts list, should add following explanation.

Determine that with statistical method the characteristic dimension of tolerance should make with statistics Working Procedure Controlling method.Have only that statistical tolerance is only suitable when measured value satisfies following the requirement.1) Working Procedure Controlling figure shows that relevant manufacturing process is controlled.2) skew of the relative nominal value of average is not more than 10% of specification tolerance.3) C _PkBe at least 1.0, its degree of confidence is 90%.

In part data, have only in the time of need controlling the mean shift of parts characteristic dimension, just use this explanation.

Adopt statistical analysis technique to be met the tolerance of matching requirements if having only, and when not needing to part that skew is controlled, on drawing, mark with the mode of similar Figure 13.In parts list, answer additional classes like following explanation.

Determine that with statistical method the characteristic dimension of tolerance should make with statistics Working Procedure Controlling method.Have only that statistical tolerance is only suitable when the operation measured value satisfies following the requirement.1) Working Procedure Controlling figure shows that relevant manufacturing process is controlled.2) C _pValue is at least 1.0, and its degree of confidence is 90%.

Can (X, Y carry out statistical appraisal respectively to control, mean shift and process capability respectively on Z) independently in each suitable coordinate axis.Figure 15 to 17 shows from the conversion of circle tolerance to monotropic first specification tolerance limit.Have only the situation that manufacturing process or one measured value separately batch is distribution, statistical tolerance is only suitable.If the distribution of operation is acceptable, some independent observed quantities can not be disallowable because of surpassing the statistical tolerance specification limit.

The Fundamentals of Mathematics of above-mentioned analytical approach and parts acceptance technology depend on the use to known production process ability.In preliminary stage of preparation or changing to when being defined as adding up the operation of control, preferably utilize above-mentioned statistical technique, to relax the tolerance limit of parts.Use batch checking and accepting technology can assess part, still can guarantee the qualification rate of assembly parts according to these tolerances.Batch check and accept is to be based upon to adopt batch qualitative index (LQI) on the basis of short-term ability evaluation.The calculating of LQI and C _PkIdentical, but operation needs not to be and can add up control.Mean shift and LQI that parts sample during production is criticized is used for described crowd estimate, to estimate the drawing tolerance.After setting up tolerance with acceptable confidence level, under this confidence level, part is criticized and is satisfied tolerance, and then whole batch is acceptable.If part is criticized any one that does not satisfy in LQI or the mean shift requirement, then must measure all parts.Can will influence the remaining parts criticized of part reject by those parts of checking and accepting, and serve as according to recomputating LQI and mean shift with remaining parts.

Obviously, those skilled in the art's instructions other the many distortion and variation that can draw disclosed preferred embodiment thus.Therefore, should be understood that these distortion, variation and equivalent processes all drop in design of the present invention and the scope, this is defined by accompanying power claim.

Claims (5)

1. assembly parts, it has one group of predetermined dimensional tolerence, and these assembly parts are made up of a plurality of parts that several respectively have one group of individual tolerance, and described assembly parts comprise:

Form at least two parts of described assembly parts, it is overall that they take from different parts respectively, and its predetermined dimensional tolerence has statistical nature;

Make the described parts keeper of the adjacent parts of relative positioning in assembly parts each other, described keeper is processed on described parts with mean shift and Deviation Control Method;

Described parts totally have such statistical nature, and it has determined the overall acceptance probability of the parts that are assembled into described assembly parts.

2. assembly parts as claimed in claim 1, wherein,

Described parts are based on the project organization of parts, and it has the nominal accessory size, comprise the location dimension of the keeper of described parts;

Adopt C _PkThe manufacturing process of 〉=A processes keeper on described parts, the average of the location dimension of described position components part does not exceed the predetermined percentage of the margin tolerance of parts design,

Wherein x is approximately less than 20, and A is at least 1.0, and

$A=\frac{.927(1-{\mathrm{\&eta;}}^{*}+\sqrt{1-{\mathrm{\&eta;}}^{*}+{\mathrm{\&eta;}}^{*2}/3})}{.927(1-{\mathrm{\&eta;}}_0+\sqrt{1-{\mathrm{\&eta;}}_0+{\mathrm{\&eta;}}_0^2/3})+({\mathrm{\&eta;}}_0-{\mathrm{\&eta;}}^{*})(\sqrt{n}+\sqrt{3})}$

Here η ^*=2x/100, η ₀Be preliminary election mean shift limit band, it equals the twice of mean shift, and n is the number of comprehensive tolerance in described assembly parts.

3. assembly parts as claimed in claim 1, wherein,

The average of described element size does not exceed the x% of the margin tolerance of described Element Design, and the relational expression of described element size tolerance and described build-up tolerance is as follows:

T wherein _Assembling=described build-up tolerance

t _i=described component tolerances

M (n) correction factor, and

$M\left(n\right)=\frac{.927(1-{\mathrm{\&eta;}}_0)+{\mathrm{\&eta;}}_0\sqrt{n}+.927\sqrt{1-{\mathrm{\&eta;}}_0+{\mathrm{\&eta;}}_0^2/3}+{\mathrm{\&eta;}}_0\sqrt{3}}{2}$

Here η ₀Be preliminary election mean shift limit band, promptly for 10% the mean shift limit, η ₀=0.2, n is the number of comprehensive tolerance in described assembly parts.

4. assembly parts as claimed in claim 3, wherein,

When x less than or approximate 20, n is between 2 and 30 the time, correction factor M (n) is approximate to be between 1 and 2.

5. assembly parts as claimed in claim 1, wherein,

The parts that are used for described assembling according to the statistical study to the location dimension of the described keeper of parts and size are whether the acceptable operation that is identified for making described parts is competent and controlled, and this requires the C of the operation of the described keeper that is used for process component at least _PkBe at least 1.0; And the average of the size of the keeper of the described parts of determining with statistical method can not exceed counterpart margin tolerance 20%.

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